Simple Maps with Fractal Diffusion Coefficients

Details Simple Maps with Fractal Diffusion Coefficients Simple Maps with Fractal Diffusion Coefficients

1994-08-03

arxiv.org/abs/chao-dyn/9407018v2

Phys. Rev. Lett. 74 (1995) 387

Nonlinear Sciences

Chaotic Dynamics

4 pages, LaTeX with REVTeX, and 3 figures, Postscript, in uuencoded tar file. to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.74.387

We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron equation. For Markov partition values of the slope, we relate the diffusion coefficient to eigenvalues of the topological transition matrix. The diffusion coefficient obtained shows a fractal structure as a function of the slope of the map. This result may be typical for a wide class of maps, such as two dimensional sawtooth maps.

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